A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension
How to cite: Wang, X.; Dai, W.; Biswas, A. A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension. Preprints 2024, 2024100770. https://doi.org/10.20944/preprints202410.0770.v1 Wang, X.; Dai, W.; Biswas, A. A Conservative and Compact Finite Difference Scheme for the Sixth-Order Boussinesq Equation with the Surface Tension. Preprints 2024, 2024100770. https://doi.org/10.20944/preprints202410.0770.v1
Abstract
In this study, we propose a conservative and compact finite difference scheme designed to preserve both the mass change rate and energy for solving the sixth-order Boussinesq equation with the surface tension. Theoretical analysis confirms that the proposed scheme achieves second-order accuracy in temporal discretization and fourth-order accuracy in spatial discretization. The solvability, convergence, and stability of the difference scheme are rigorously established through the application of the discrete energy method. Additionally, a series of numerical experiments are conducted to illustrate the effectiveness and reliability of the conservative scheme for long-time simulations.
Keywords
Boussinesq equation; convergence; conservation; stability
Subject
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)